Method and apparatus for aiding in solution of three-dimensional fire control problems

ABSTRACT

1. Apparatus for aiding in the solution of a fire control problem for a weapon adapted to attack an underwater target, said weapon being of a type traveling along an air-trajectory to a point on the surface of the water in the vicinity of the target and thence along an underwater trajectory in response to a self contained control, said control causing the weapon to have predetermined characteristics affecting the likelihood of hitting a target under various spacial and relative motion situations, said apparatus comprising; A. AN AIR-TRAJECTORY DISPERSION ERROR CURVE REPRESENTING PROBABLE AREA WITHIN WHICH THE WEAPON WILL ENTER THE WATER FOR A GIVEN AIMPOINT, B. A RIGID ELEMENT INCLUDING C. A REFERENCE MARKER REPRESENTING A POSITION DATUM OF THE TARGET, SAID POSITION DATUM CONSISTING OF THE AZIMUTHAL COORDINATES ONLY OF THE TARGET POSITION; AND D. A STACK OF PARALLEL SPACED TRANSPARENT MEMBERS, THE INDIVIDUAL MEMBERS OF SAID STACK EACH REPRESENTING THE AREA ON THE SURFACE OF THE WATER WITHIN WHICH THE WEAPON SHOULD ENTER THE WATER IN ORDER TO HAVE A DESIRED LIKELIHOOD OF HITTING A TARGET AT SAID DATUM POSITION FOR A DIFFERENT DEPTH LEVEL OF A PREDETERMINED SERIES OF SEPARATED DEPTH LEVELS, SAID INDIVIDUAL MEMBERS OF THE STACK BEING STACKED IN ORDER OF THE DEPTH LEVEL THEY REPRESENT, AND E. THE CONSTRUCTION AND ARRANGEMENT BEING SUCH THAT SAID STACKED MEMBERS PROVIDE A THREE-DIMENSIONAL IMAGE OF DESIRED WATER ENTRY AREAS FOR DIFFERENT TARGET DEPTHS IN SUPERPOSED RELATIONSHIP TO THE AIR-TRAJECTORY DISPERSION ERROR CURVE, SAID DISPERSION ERROR CURVE AND SAID RIGID ELEMENT BEING MOVABLE RELATIVELY WHEREBY THE EFFECT OF VARIOUS ADJUSTMENTS OF AIMPOINT RELATIVE TO THE TARGET POSITION DATUM UPON THE FIRE CONTROL PROBLEM SOLUTION FOR VARIOUS DEPTH LEVELS OF THE TARGET MAY BE READILY ENVISIONED.

United St Maudlin METHOD AND APPARATUS FOR AIDING 1N SOLUTION OF THREE-DIMENSIONAL FIRE CONTROL PROBLEMS Lloyd Z. Maudlin, Los Angeles, Calif.

[73] Assignee: The United States of America as represented by the Secretary of the Navy, Washington, DC.

[22] Filed: Apr. 23, 1964 {21] Appl. No.: 363,676

[75] Inventor:

Primary Examiner-Maynard R. Wilbur Assistant Ii.\'amim'rH. A. Birmiel Attorney, Agent, or l"irmRichard S. Sciascia; Ervin Johnston EXEMPLARY CLAIM 1. Apparatus for aiding in the solution of a fire control problem for a weapon adapted to attack an underwater target, said weapon being of a type traveling along an air-trajectory to a point on the surface of the water in the vicinity of the target and thence along an underwater trajectory in response to a self contained control, said control causing the weapon to have predetermined characteristics affecting the likelihood of hitting a target under various spacial and relative motion situations, said apparatus comprising;

a. an air-trajectory dispersion error curve representing probable area within which the weapon will enter the water for a given aimpoint,

b. a rigid element including 0. a reference marker representing a position datum of the target, said position datum consisting of the azimuthal coordinates only of the target position; and

d. a stack of parallel spaced transparent members, the individual members of said stack each representing the area on the surface of the water within which the weapon should enter the water in order to have a desired likelihood of hitting a target at said datum position for a different depth level of a predetermined series of separated depth levels, said individual members of the stack being stacked in order of the depth level they represent, and

e. the construction and arrangement being such that said stacked members provide a three-dimensional image of desired water entry areas for different target depths in superposed relationship to the air-trajectory dispersion error curve, said dispersion error curve and said rigid element being movable relatively whereby the effect of various adjustments of aim-point relative to the target position datum upon the fire control problem solution for various depth levels of the target may be readily envisioned.

6 Claims, 5 Drawing Figures 34a Pt-UENTED W 1 31975 883 .OTU

SHEET 105 2 INVENTOR. LLOYD Z. MAUDLIN y dw/ ATTORNEY.

METHOD AND APPARATUS FOR AIDING IN SOLUTION OF THREE-DIMENSIONAL FIRE CONTROL PROBLEMS The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.

This invention relates to methods and apparatus for aiding in the solution of fire control problems in connection with anti-submarine warfare weapons, and has particular utility in connection with an anti-submarine weapon of the type which travels along an airtrajectory from a launching station toward a selectively chosen aim-point on the surface of the water, and which after striking the water enters the water and travels along a three-dimensional underwater trajectory under control of a self-contained homing guidance system. The invention also generally relates to apparatus for presenting fire control data concerning the underwater capability of an anti-submarine weapon as a function of depth of target.

The prior art approach in solving fire control problems for weapons of the type referred to has been to establish broad doctrinaire formulations for the selection of aim point and depth setting of the weapon. For example, the authorities responsible for fire control practices would establish a nominal distance by which the aim point of the weapon should lead the target, and this nominal target lead distance would be applied in the solution of all fire control problems. In the selection of depth setting of the weapon, the value of depth setting which most closely corresponded to the estimated depth of the target was selected.

-On the other hand, weapon designers and weapon performance analysts have long known that various important factors affecting the probability of success of the weapon as a function of the depth of the target, are not considered in the prior art approach. Many of these factors have been brought out in simulation laboratory studies in which operation of the weapon has been simulated. For example, most underwater weapons have acoustic homing guidance systems, and the weapon is steered along a predetermined three-dimensional underwater target search trajectory under control of a steering programmer, until the target senser picks up the target. Since the target senser has directional sensitivity characteristics, the form of the target search trajectory is very significant in defining the capability of the weapon as a function of depth of the target. The problem is further aggravated in the case of weapons launched along air-trajectories under the control of fire control systems responsive to shipboard sonars, because of the shot dispersion errors associated with both the fire control equipment and the air flight characteristics of the weapon. It is believed a fair judgment, that because of failure to consider these factors the prior art fire control solution practices can result in seemingly good firing solutions which actual result in a very low probability of success.

Although fire control data has been available which reflects these factors and which could help in the evaluation of the probability of success of a given firing solution, presenting this data in a form that is suitable to aid in the solution of fire control problems has been a serious problem prior to the present invention, because of the obvious requirement for rapid interpretation. Various tables and single-plane charting techniques have been tried, but despite their indicated utility, they have not found any appreciable scope of use beyond that made by weapons performance analysts themselves. To a large extent the reluctance to employ such tables and charts is believed to be the result of their failure to present the data in a manner that can be readily associated with its physical significance.

Recognizing the foregoing problems and seeking their solution, the objectives of the present invention include provision of:

1. Methods and apparatus for aiding in the solution of a fire control problem for an anti-submarine weapon which travels along an air-trajectory and thence along an underwater trajectory, which enables an operator to make fast comprehensive evaluations of the effectiveness of a given firing solution as a function of the depth of the target.

2. An apparatus in accordance with the previous objective which enables an operator to define an over-all probability of success of the weapon for a given firing solution, which reflects the combined effects of dispersion errors of the fire control equipment and the airflight of the weapon, and the effects of the underwater capability of the weapon as a function of depth.

3. Novel apparatus for presenting complex fire control data concerning the underwater capability of an anti-submarine weapon as a function of depth, which presents the data in a manner that can be readily associated with its physical significance.

Other objects and many of the attendant advantages of this invention will be readily appreciated as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings wherein:

FIG. 1 is a perspective view of the apparatus forming the subject of the invention with the parts shown in exploded positions, as distinguished from their normal position during use of the apparatus;

FIG. 2 is a side elevation of the apparatus of FIG. 1, in reduced scale, and taken in the direction of arrow 2, FIG. 1, with the parts shown in their normal positions during use;

FIG. 3 is an enlarged plan view taken along line 33, FIG. 2; and

FIGS. 4 and 5 are enlarged top plan views of FIG. 2 in which the parts are in different relative positions, certain analytic curves being omitted for purposes of clarity, and others being shown in broken line to provide distinction.

The apparatus hereinafter described is intended to be employed as a fire control solution aid in connection with a weapon of the type disclosed in the patent application of Orville J. Saholt et al. entitled Rocket Thrown Missile," Ser. No. 8201, filed Feb. 11, 1960, and which is delivered to the aim-point by rocket propulsion. This weapon, which is commonly known as the ASROC weapon, travels from the point at which it is launched along a rocket propulsion air-trajectory toward a selectively chosen aim-point on the surface of the water. After striking the water the weapon enters the water and travels along a three-dimensional underwater trajectory under the steering control of a self contained underwater homing system. The underwater guidance system is further characterized by its inclusion of a steering programmer which steers the weapon along a predetermined form of helical target search trajectory until the target senser of the homing system picks up the target, whereupon the weapon homes toward the target under homing guidance control. The steering programmer of a particular design of the ASROC weapon is pre-settable at the time of launching to start the helical search trajectory at any one of the following depths: 150 feet, 250 feet, 450 feet, 650 feet, or 900 feet. The specific form of helical search trajectory of this design of the weapon consists of the weapon following a steep dive to the-preset helical search trajectory starting depth, whereupon the weapon starts to follow a helical trajectory of predetermined direction of turn and radius of helix, and thence gradually winds down along such trajectory to a predetermined floor depth, and thence alternately winds up to a ceiling depth above the preset depth, and winds down to the floor depth, all along the same gradual helical trajectory. An example of a steering programmer produced helical form of target search trajectory, which is essentially the same as that described except as to specific depths and sequences, is disclosed in the patent application of Seth G. Fisher et al. entitled Torpedo Steering Control System, Ser. No. 94,095, filed Mar. 7, 1961.

Referring now to the drawing and in particular to FIG. 1, the subject of the invention comprises apparatus 10, the particular embodiment illustrated being adapted for the design of ASROC weapon having the specific form of helical target search trajectory described. Broadly, apparatus comprises a card 12 on which is imprinted a combined air trajectory and tire control dispersion error diagram 14, or more simply a dispersion error diagram. This diagram represents a probabilistic relationship between the aim-point on the surface of the water at which the weapon is aimed at the time of launching, and the bounds of areas on the surface of the water within which the weapon is likely to strike the water, as determined by various dispersion errors inherent to the weapon system. A stack of curve members 16 represents a probabilistic relationship between the bounds of areas on the surface of the water within which the weapon may enter the water and the likelihood of hitting a target at various depths, as determined by the weapons underwater capability, and in particular the capability of the target senser of the homing guidance system to pick up the target during the period the missile travels along the helical form of target search trajectory. Further, the stack of curves are adapted for use of the weapon against a specific class of submarine traveling at a specific speed and executing a specific maneuver. The embodiment illustrated in the drawing is for a common class of US. Navy submarine following a straight course at a constant depth with a speed of 20 knots. As shown in FIG. 2, card 12 is placed on a table top 18, or other flat surface, with the shot placement dispersion diagram 12 facing upward, and stack of curve member 16 is then placed over the card. Card 12 is provided with a manipulation tab 20 in order to facilitate relative positioning of the card and the stack of curve members in planes parallel to surface of the table.

Referring now to FIG. 3, dispersion error diagram 14 includes a centrally disposed point A representing the aim point. An arrow B disposed at the bottom of the diagram represents the direction of motion of the target. A 30 percent probability dispersion error curve 220, is drawn in a predetermined scale representing distances on the surface of the water. The probability relationship represented by curve 22a is as follows: If a weapon is launched from a launching station with point A as the aim point set into the fire control equipment controlling the launching, there is a 30 percent probability that the weapon would strike the water within the area bounded by the curve. Curves 22b and 220 represent like probability relationships, but for 50 percent and percent probability values, respectively. A graduated linear scale 24 passes through point A in the direction of arrow B. Another graduated linear scale 26 passes through point A in a direction perpendicular to scale 24. The shapes of curves 22a, b, c are determined by conventional simulation laboratory techniques of simulating the operation of the fire control equipment, including target senser, tracking computer, and launcher position control servos; and integrating the results of ballistic tests for determining air-flight dispersion errors with the results of the simulation studies.

Stack of curve members 16, best shown in FIGS. 1 and 2, comprises a base panel 28 of clear transparent plastic. A cross-mark C, inscribed on the panel, represents an azimuthal plane target position datum, which defines the location of the target by magnitudes of a pair of coordinates defining a position in azimuth, only. Thus, position datum C represents a vertical axis in the water and defines the location of the target as disposed somewhere along this axis with the depth of the target undefined. It is to be further understood that position datum C represents the position of the target at the moment the weapon enters the water at the conclusion of its air trajectory, and thus must be predicted, by conventional fire control solution practices, from a position datum for the moment of launching. An arrow D, also inscribed on the panel, represents the direction of motion of the target. A position datum post 30, made of clear plastic, is affixed to panel 28 in vertical alignment over position datum C. Four vertical support posts 32, of like material, are affixed to panel 28 at various locations convenient for the support of the stack of curve members. Mounted to the datum post and to the support posts are a set of water entry position 50 percent probability curve members, or simply hit probability curve members 34a (having two separated sections), 34b, 34c, 34d, 34e and 34f. The probability relationship represented by curve member 34c is as follows: The curve member represents an area on the surface of the water in the same scale as that employed with diagram 12, and if a weapon strikes the water within such area it has a 50 percent probability of hitting a target disposed at position datum C and at the helical search trajectory starting depth. The phrase hitting the target used in the latter statement is not limited to situations in which the weapon physically strikes the target, but includes any attack against a target which is deemed successfuL'such as the exploding of a proximity fuse in sufficiently close relationship to the target to prevent it from performing its mission. Curve members 34a, 34b, 34d, 34e and 34f represent like probability relations, but for target depths feet above the preset helical search trajectory starting depth, 50 feet above such preset depth, 50 feet below such preset depth, 100 feet below such preset depth, and I50 feet below such preset depth, respectively. It is to be noted that in the instance of the hit probability curve members, each member of the set represents a probability relationship having the same numerical probability value 50 percent. This is in contradistinction to the previously described family of dispersion error curves in which each curve represented a different one of 30 percent, 50 percent and 70 percent probability values. The curve members are stacked in the same order as target depth of the probability relationships which they individually represent, and are spaced apart in scaled relationship to the target depths. The scale determining this separation is so chosen that i when the person using the apparatus looks down upon the stack along a line of sight E, FIG. 2, in alignment with the datum post, he sees the stack of curves with three dimensional perspective which gives the user a feeling of the relative spacing of each curve member. The shape of curve members 34a, b, c, etc. are determined by conventional simultation laboratory techniques of simultating the operation of the underwater homing guidance system.

The operation and use of apparatus will be illustrated by an exemplary fire control problem in which it is assumed that the best available data concerning the depth of a target is that it is disposed somewhere in a range of depths extending from a 400 foot depth down to a 600 foot depth, and that a choice has been made to preset the weapon to start its helical search trajectory at a depth of 450 feet. Apparatus 10 will then be used to aid in selecting an aim point relative to the predicted position datum of the target. The stack of curve members 16 is placed over card 12 with arrows B and C aligned in a common direction. The operator looks down on the apparatus along a line of vision generally aligned with the datum post, and grasps the stack of curve members with one hand to hold it in stationary relation to his line of vision, and grasps the manipulation tab 20 of card 12 with the other hand for moving same relative to stack of curve member 16.

The edges of the curve member 34 will tend to appear to the operator as a three-dimensional irregularly shaped surface of a volume, and this surface and dispersion error diagram 14 may be simultaneously observed by the operator in their superposed relation. The shape of this surface is hereafter referred to as a hit probability volume. Then, as a mental step in the use of apparatus 10, the operator envisions the various depth stratum of the hit probability volume as corresponding to the physical underwater depth stratum in the fire control problem associated with the respective curve members, whose edges form the discrete shapes of stratum of the hit probability volume. For example, curve member 34c represents a probability relation for a target depth at the preset helical search trajectory starting depth, which is assumed to be 450 feet for purposes of the problem, and therefore the operator envisions the part of the hit probability volume formed by the edge of curve member 34c as corresponding to a 450 foot depth level. Similarly curves 34a, 34b, 34d, 342 and 34f are envisioned as corresponding to depth levels of 350 feet, 400 feet, 500 feet, 550 feet, and 600 feet, respectively. Since the problem involves a target known to be confined between 400 feet and 600 feet, only the corresponding strata of the hit probability volume are of interest to the operator.

The operator then moves card 12 relatively to stack of curve member 16 while continuing to look down on the stack, and tries to find the relative position of the card and stack at which the greatest proportion of the strata of interest of the hit probability volume is in superposed relation with the percent dispersion error curve 22c on the dispersion error diagram. An observation that the surface of the hit probability volume corresponding to a particular underwater depth stratum fully encompasses the dispersion error curve represents a definite probability of the overall effectiveness of the weapon against a target at such depth stratum for a particular aim point. For example, FIG. 4 shows stack of curves l6 and error dispersion diagram 14 in their relative positions with aim-point A 500 yards ahead of position datum C, in the direction of target motion. The edges of curves 34b and 34c which correspond to the 400 foot and 450 foot underwater depth stratums (as indicated on the drawing in parenthesis), both encompass 70 percent dispersion error curve 22c. This means that there is in excess of a 70 percent probability that a weapon fired at an aim point 500 yards ahead of the position datum would strike the surface of the water in an area in which the weapon would have a further and distinct 50 percent probability of hitting a target located at the 400 or 450 foot depth stratum. In accordance with the general rule for combining distinct probabilities relating to the same event, the overall hit probability is determined by multiplication of these probability values and is equal to a probability in excess of 35 percent (0.50 X 0.70 0.35). Such an overall hit probability reflects both the dispersion error effects, represented by diagram 14, and the underwater capability effects represented by stack of curve members 16. An observation that the surface of the hit probability volume corresponding to a particular underwater depth is insufficiently large to cover a dispersion error curve indicates that the overall hit probability for the corresponding depth is less than that represented by a surface which encompasses the dispersion curve. A rough comparison may be made between the overall hit probability for such a situation in which the surface does not cover the dispersion error curve and the overall hit probability for the situation in which the surface encompasses the error dispersion curve, by observing and estimating the percentage of the dispersion error curve which is encompassed by the surface of the hit probability volume. For example, curve 34f, FIG. 4, representing the 600 foot depth covers roughly 30 percent of dispersion error curve 22c, shown by crosshatching. By making the assumption of uniform probability of distribution of shots within dispersion error curve 22c, it follows that the overall hit probability at 600 feet is 30 percent of the previously determined 35 percent overall hit probability that exists where the surface of the hit volume fully encompasses the dispersion error curve, and is therefore roughly equal to a 10 percent overall hit probability. Moving card 14 to a relative position in which aim-point A is 700 yards ahead of position datum B, FIG. 5, results in no substantial change in the overall hit probability for a target at the 400 or 450 foot depth stratum since the edges of curve members 34b and 34c still fully encompass dispersion error curve 220. However, curve 34fnow encompasses approximately 50 percent of curve 22c, shown by cross-hatching, indicating that the overall hit probability for a target at the 600 foot depth stratum has been increased to roughly 15 percent. After the operator is satisfied that he has found the relative position of card and stack of curves which gives the optimum overall hit probability over the depth strata of interest, the right angle coordinate distance from position datum B to aim-point A may be read as the points along scales 24 and 26 in right angle alignment with the datum post.

Apparatus 10 can be similarly employed as an aid in fire control problem solving to select a combination of the aim-point and the depth setting for the helical trajectory starting depth. In this case the operator performs the additional mental steps of envisioning the hit probability volume as corresponding to different underwater depth strata in accordance with the different possible choices of helical trajectory starting depths. Another use of apparatus 10 is in connection with launching equipment for the ASROC weapon of the type disclosed in U.S. Pat. No. 3,106,132 to E. E. Biermann et al., entitled Launcher in which the weapon may be launched singly or in substantially simultaneously launched pairs. For this purpose another apparatus like apparatus 10 is adapted to give hit probabilities and dispersion error curves for such multiple launching. The operator then alternately uses the apparatus representing a single launching and the apparatus representing the multiple launching and determines the relative advantage of the multiple launching from a comparison of the respective overall hit probabilities that exist for the underwater depth strata of interest.

While the previous description of the use of the apparatus was necessarily done by reference to a singleplane charts of the type used in the prior art, it is to be understood that it is an important feature of the present invention that a feeling of a three-dimensional surface is given to the operator, and that this three-dimensional surface presents the data concerning the underwater capability of the weapon at various depths, with the effect that hit probability as a function of various target depths is shown in the dimension corresponding to the underwater depth strata in the problem. As a result, with brief training, a person can make nearly instantaneous comprehensive interpretations of the effect of various possible firing solutions from the relative position of the hit probability volume as a whole, and without the discrete mental steps needed with single-plane charts.

Obviously many modifications and variations of the present invention are possible in the light of the above teachings. It is therefore to be understood that within the scope of the appended claims the invention may be practiced otherwise than as specifically described.

What is claimed is:

1. Apparatus for aiding in the solution of a fire control problem for a weapon adapted to attack an underwater target, said weapon being of a type traveling along an air-trajectory to a point on the surface of the water in the vicinity of the target and thence along an underwater trajectory in response to a self contained control, said control causing the weapon to have predetermined characteristics affecting the likelihood of hitting a target under various spacial and relative motion situations, said apparatus comprising;

a. an air-trajectory dispersion error curve representing probable area within which the weapon will enter the water for a given aimpoint,

b. a rigid element including c. a reference marker representing a position datum of the target, said position datum consisting of the azimuthal coordinates only of the target position; and

d. a stack of parallel spaced transparent members,

the individual members of said stack each representing the area on the surface of the water within which the weapon should enter the water in order to have a desired likelihood of hitting a target at said datum position for a different depth level of a predetermined series of separated depth levels, said individual members of the stack being stacked in order of the depth level they represent, and

e. the construction and arrangement being such that said stacked members provide a three-dimensional image of desired water entry areas for different depths in superposed relationship to the airtrajectory dispersion error curve, said dispersion error curve and said rigid element being movable relatively whereby the effect of various adjustments of aim-point relative to the target position datum upon the fire control problem solution for various depth levels of the target may be readily envisioned.

2. Apparatus in accordance with claim 1 wherein,

f. said marker comprises a post in perpendicular relationship to said parallel member and said stack is so constructed to provide said three-dimensional image when viewed from a line-of-sight generally aligned with said post.

3. Apparatus in accordance with claim 1 wherein,

g. said air-trajectory dispersion curve further comprising graduated scale means adapted to cooperate with said marker of the rigid element to provide a reading of the adjustment of aimpoint relative to target position datum.

4. Apparatus in accordance with claim 1,

h. said air-trajectory dispersion curve being defined as a closed curve about the aim point such that in a probable distribution of a large number of shots under the same conditions a predetermined percentage will fall within the curve and the rest outside the curve, and the i. the individual transparent members of the stack of members being shaped as a closed curve encompassing all points on the surface of the water at which the weapon, upon entering the water thereat, would have a probability of hitting the target of at least a predetermined probability value, whereby superposed portions of individual transparent members and said shot dispersion curve represents an indicia of combined effectiveness of airflight trajectory and underwater trajector for a given target position datum.

5. Apparatus for aiding in the solution of a fire con-- a. an air-trajectory dispersion error curve represent-- ing the probable area within which the weapon will enter the water for a given aimpoint,

b. transparent means for providing a threedimensional image adapted for simultaneous viewing in superposed relationship to said shot dispersion chart, said image consisting of a plurality of individual images representing discrete areas on the surface of the water and including a reference marker representing a position of the target, said position datum comprising the azimuthal coordinate information, only, of the target position, said individual images each representing the desired area on the surface of the water within which the weapon should enter the water in order to have a desired likelihood of hitting a target at said position for a different depth level of a predetermined series of separated depth levels, said individual images being arranaged in said three-dimensional image in order of their corresponding depth,

c. said air-trajectory dispersion error curve and said threedimensional image being relatively movable, whereby the combined effect of air-trajectory dispersion error and target depth may be envisioned for various adjustment of aim point relative to the position datum.

6. A device for use in presenting data for the solution of three dimensional fire control problems in conjunction with an acoustic torpedo of the type having predetermined underwater trajectory characteristics, comprising;

a. a reference marker representing a position datum of the target, said position datum comprising the azimuthal coordinate information, only, of the target position, and

b. a stack of parallel spaced members in fixed spacial relationship to said reference marker, each member of said stack corresponding to a different depth level of a predetermined series of separated depth levels, each member of said stack being shaped in accordance with a hit probability curve comprising a plot relative to the position datum encompassing all points on the surface of the water at which the weapon, upon entering the water, would have a probability of hitting a target at the position datum in the corresponding depth level of at least a predetermined probability value,

said members of said stack being disposed in order of their corresponding depth level. 

1. Apparatus for aiding in the solution of a fire control problem for a weapon adapted to attack an underwater target, said weapon being of a type traveling along an air-trajectory to a point on the surface of the water in the vicinity of the target and thence along an underwater trajectory in response to a self contained control, said control causing the weapon to have predetermined characteristics affecting the likelihood of hitting a target under various spacial and relative motion situations, said apparatus comprising; a. an air-trajectory dispersion error curve representing probable area within which the weapon will enter the water for a given aimpoint, b. a rigid element including c. a reference marker representing a position datum of the target, said position datum consisting of the azimuthal coordinates only of the target position; and d. a stack of parallel spaced transparent members, the individual members of said stack each representing the area on the surface of the water within which the weapon should enter the water in order to have a desired likelihood of hitting a target at said datum position for a different depth level of a predetermined series of separated depth levels, said individual members of the stack being stacked in order of the dEpth level they represent, and e. the construction and arrangement being such that said stacked members provide a three-dimensional image of desired water entry areas for different depths in superposed relationship to the air-trajectory dispersion error curve, said dispersion error curve and said rigid element being movable relatively whereby the effect of various adjustments of aim-point relative to the target position datum upon the fire control problem solution for various depth levels of the target may be readily envisioned.
 2. Apparatus in accordance with claim 1 wherein, f. said marker comprises a post in perpendicular relationship to said parallel member and said stack is so constructed to provide said three-dimensional image when viewed from a line-of-sight generally aligned with said post.
 3. Apparatus in accordance with claim 1 wherein, g. said air-trajectory dispersion curve further comprising graduated scale means adapted to cooperate with said marker of the rigid element to provide a reading of the adjustment of aim point relative to target position datum.
 4. Apparatus in accordance with claim 1, h. said air-trajectory dispersion curve being defined as a closed curve about the aim point such that in a probable distribution of a large number of shots under the same conditions a predetermined percentage will fall within the curve and the rest outside the curve, and the i. the individual transparent members of the stack of members being shaped as a closed curve encompassing all points on the surface of the water at which the weapon, upon entering the water thereat, would have a probability of hitting the target of at least a predetermined probability value, whereby superposed portions of individual transparent members and said shot dispersion curve represents an indicia of combined effectiveness of air-flight trajectory and underwater trajector for a given target position datum.
 5. Apparatus for aiding in the solution of a fire control problem for a weapon adapted to attack an underwater target, said weapon being of a type traveling along an air-trajectory to a point on the surface of the water in the vicinity of the target and thence along an underwater trajectory in response to a self-contained control, said control causing the weapon to have predetermined characteristic affecting the likelihood of hitting a target under various spacial and relative motion situations, said apparatus comprising, a. an air-trajectory dispersion error curve representing the probable area within which the weapon will enter the water for a given aimpoint, b. transparent means for providing a three-dimensional image adapted for simultaneous viewing in superposed relationship to said shot dispersion chart, said image consisting of a plurality of individual images representing discrete areas on the surface of the water and including a reference marker representing a position of the target, said position datum comprising the azimuthal coordinate information, only, of the target position, said individual images each representing the desired area on the surface of the water within which the weapon should enter the water in order to have a desired likelihood of hitting a target at said position for a different depth level of a predetermined series of separated depth levels, said individual images being arranaged in said three-dimensional image in order of their corresponding depth, c. said air-trajectory dispersion error curve and said three-dimensional image being relatively movable, whereby the combined effect of air-trajectory dispersion error and target depth may be envisioned for various adjustment of aim point relative to the position datum.
 6. A device for use in presenting data for the solution of three dimensional fire control problems in conjunction with an acoustic torpedo of the type having predetermined underwater trajectory characteristics, comprising; a. a reference marker representing a position datum of the target, Said position datum comprising the azimuthal coordinate information, only, of the target position, and b. a stack of parallel spaced members in fixed spacial relationship to said reference marker, each member of said stack corresponding to a different depth level of a predetermined series of separated depth levels, each member of said stack being shaped in accordance with a hit probability curve comprising a plot relative to the position datum encompassing all points on the surface of the water at which the weapon, upon entering the water, would have a probability of hitting a target at the position datum in the corresponding depth level of at least a predetermined probability value, said members of said stack being disposed in order of their corresponding depth level. 